In Exercise 6.10, we learn that the percent of free throws made in the NBA (National Basketball Association) has been about 75% for the last 50 years. If we take random samples of free throws in the NBA and compute the proportion of free throws made, what percent of samples of size n = 200 will have a sample proportion greater than 80%? Use the fact that the sample proportions are normally distributed and compute the mean and standard deviation of the distribution.

Exercise 6.10

Usually, in sports, we expect top athletes to get better over time. Weexpect future athletes to run faster, jump higher, throw farther. One thing has remained remarkably constant, however. The percent of free throws made by basketball players has stayed almost exactly the same for 50 years. For college basketball players, the percent is about 69%, while for players in the NBA (National Basketball Association) it is about 75%. (The percent in each group is also very similar between male and female basketball players.) In each case below, find the mean and standard deviation of the distribution of sample proportions of free throws made if we take random samples of the given size.